Equivalent Fractions: A fraction represents a part of the entire. A fraction has two parts, called the numerator and the denominator. Equivalent Fractions have a different numerator and the denominator, but they have the indistinguishable absolute valuate. For example, \(\frac{2}{4}\) and \(\frac{5}{10}\) are capable the evaluate \(\frac{1}{2}\). Then, \(\frac{2}{4}\) and \(\frac{5}{10}\) are called equivalent fractions. In that clause, we shall discuss equivalent fractions.
Fractions:
The numbers of the form \(\frac{a}{b}\) where \(a\) and \(b\) are non-zero integers, which are called fractions.
Here, \(a{\mkern 1mu} \to \) Numerator and \(b{\mkern 1mu} \to \) Denominator.
Examples: \(\frac{2}{4},\,\,\frac{5}{{10}},\,\frac{1}{4},\,\frac{3}{{17}}…\) are fractions.
The above figure has been divided into \(7\) equal parts. Extinct of these \(7\) equal parts, \(4\) parts are shaded. Thus, the shaded dower represents iv-sevenths .
Numerically, it is denoted as \(\frac{4}{7}\).
Here, \(\frac{4}{7}\) is a divide and foursome – sevenths is a fractional number.
Types of Fractions:
There are \(3\) different types of fractions:
\(1\). Proper Fractions:
A fraction whose numerator is less than its denominator is called a proper fraction.
Examples: \(\frac{2}{4},\,\,\frac{5}{{10}},\,\frac{1}{4},\,\frac{3}{{17}}\) etc., are all proper fractions.
Note: Each appropriate fraction is to a lesser degree \(1.\)
\(2\). Unfit Fractions:
A fraction whose numerator is greater than its denominator is called an indecent fraction.
Examples: \(\frac{5}{4},\,\,\frac{{13}}{{10}},\,\frac{{11}}{7},\,\frac{{23}}{{17}}\) etc., are wholly improper fractions.
\(3\). Mixed Fractions:
A combination of a whole add up and a proper fraction is called a mixed divide.
Examples:\(1\frac{2}{4},\,\,3\frac{5}{{10}},\,5\frac{1}{4},6\,\frac{3}{{17}}\), etc., are all sundry fractions.
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\(4\). Like Fractions:
The group of cardinal operating theatre more fractions with the same denominators is like fractions.
Examples: \(\frac{1}{2},\frac{2}{2},\frac{3}{2},\frac{4}{2},\frac{5}{2},\) etc., are all like-minded fractions.
\(5\). Unlike Fractions:
The aggroup of cardinal or more fractions with divergent denominators is titled Unlike Fractions.
Examples: \(\frac{1}{2},\frac{2}{4},\frac{3}{5},\frac{4}{7},\frac{5}{8},\) etc., are every last unlike fractions.
\(6\). Unit Fractions:
A unit divide is any divide with \(1\) as its numerator and a livelong number for the denominator.
Examples: \(\frac{1}{2},\frac{1}{4},\frac{1}{5},\frac{1}{7},\frac{1}{8},\) etc., are altogether unit fractions.
Annotation: The number \(1\) which rear constitute written as \(\frac{1}{1}\) has its numerator and denominator equal, is besides called a unit fraction.
Definition of Equivalent weight Fractions:
Equivalent fractions are defined as those fractions which are isoclinic to the same value irrespective of their numerators and denominators
What are Equivalent Fractions?
Two or more fractions representing the said part of a whole are called same fractions.
\(\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{{10}}\) these fractions are called equivalent fractions.
Notation that,\(\frac{1}{2} = \frac{{1 \multiplication 2}}{{2 \times 2}} = \frac{{1 \times 3}}{{2 \times 3}} = \frac{{1 \multiplication 4}}{{2 \times 4}} = \frac{{1 \times 5}}{{2 \multiplication 5}}\)
It shows that multiplying the numerator and the denominator of a fraction by the Same not-zero number does non change the value of the divide.
Likewise,\(\frac{{2 \div 2}}{{4 \div 2}} = \frac{{3 \div 3}}{{6 \div 3}} = \frac{{4 \div 4}}{{8 \div 4}} = \frac{{5 \div 5}}{{10 \div 5}} = \frac{1}{2}\)
It shows that dividing the numerator and the denominator of a fraction by the Saami non-nix number does not change the evaluate of the divide.
Rule of Equivalent Fractions:
To get a fraction equivalent to a given fraction, we multiply or divide the numerator and the denominator of the given divide by the same not-zero number.
Object lesson: The eq divide for \(\frac{3}{6}\)
\(\frac{{3 \multiplication 2}}{{6 \multiplication 2}} = \frac{6}{{12}}\) is the equivalent divide for \(\frac{3}{6}\)
\(\frac{{3 \div 3}}{{6 \div 3}} = \frac{1}{2}\) is the equivalent fraction for \(\frac{3}{6}\)
Practice Exam Questions
Equivalent Fractions Examples:
Present are few graphic examples for equivalent fractions.
Nonverbal examples for equivalent fractions are,
1. \(\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{{12}} = \frac{5}{{15}}\)
2. \(\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{{10}}\)
3. \(\frac{{100}}{{20}} = \frac{{50}}{{10}} = \frac{5}{1} = \frac{{20}}{4} = \frac{{40}}{8}\)
Distinct Methods to Determine if 2 Fractions are Like?
We should simplify the inclined fractions to find whether they are equivalent fractions or not. Simplification to get like fractions can be done until both the numerator and denominator should still atomic number 4 not-no integers.
There are various methods to check if the given fractions are equivalent or non:
1. Making the denominators the same
2. Finding the decimal variant of both the fractions
3. Cross multiplication method acting
4. Visual method
\(1\). Making the Denominators the Same:
The denominators of the fractions, \(\frac{3}{9}\) and \(\frac{6}{{18}}\) are \(9\) and \(18.\) The lowest common multiple \({\rm{Least common multiple}}\) of the denominators \(9\) and \(18\) is \(18.\) Now arrive at the denominators of both fractions \(18\) by multiplying them with suitable numbers pool.
So, \(\frac{3}{9} = \frac{{3 \multiplication 2}}{{9 \times 2}} = \frac{6}{{18}}\)
And, \(\frac{6}{{18}} = \frac{{6 \times 1}}{{18 \times 1}} = \frac{6}{{18}}\)
Note that both the fractions are equivalent to the comparable fraction \(\frac{6}{{18}}\) Thus, the given fractions are equivalent.
Bank note: If the fractions are not equivalent fractions, we can hold the greater or smaller fraction by looking the numerator of some the ensuant fractions. Hence, this method can also be used for compairing fractions.
\(2\). Finding the Denary organize of both the Fractions:
Now we can find the quantitative form of both the fractions,\(\frac{3}{9}\) and \(\frac{6}{{18}}\) to check if they give the same value.
We see, \(\frac{3}{9} = 0.33333…\)
And, \(\frac{6}{18} = 0.33333…\)
The decimal values of both the fractions are the duplicate, i.e.,\(0.33333…\)
Therefore, \(\frac{3}{9}\) and \(\frac{6}{18}\) are equivalent fractions.
\(3\). Cross Multiplication Method acting
To test whether two given fractions are equivalent or not,
let \(\frac{a}{b}\) and \(\frac{c}{d}\) be 2 given fractions.
Cross multiply the given fractions \(\frac{a}{b}\) and \(\frac{c}{d}\) atomic number 3 follows: \(a \multiplication d\) and \(b \times c\)
If \(ad\, = \,bc\) we say that \(\frac{a}{b}\) and \(\frac{c}{d}\) are equivalent fractions, other not.
To check whether \(\frac{3}{9}\) and \(\frac{6}{{18}}\) are equivalent, we cross multiply the given fractions. If both the products are the same, then the fractions are same fractions.
We hear, \(3 \multiplication 18 = 54\) and \(6 \multiplication 9 = 54\)
Take down that both the obtained products are \(54\) so the inclined fractions are equivalent fractions.
\(4\). Visual Method acting
Let USA represent for each one of the fractions \(\frac{1}{3}{\mkern 1mu}\) and \(\frac{2}{6}\) pictorially happening identical shapes and put up identify if the shady portions of both are equal or non.
We can see that the shaded portions of both the triangles are equal. Thence, the given fractions are same fractions.
Simplest Form of a Fraction
A divide is said to be in the simplest form if the \({\rm{HCF}}\) of its numerator and denominator is \(1.\)
Let the given divide be \(\frac{a}{b}\) and the \({\rm{HCF}}\) of \(a\) and \(b\)
Then, \(\frac{a}{b} = \frac{{a \div h}}{{b \div h}}\) is the simplest form.
Example: The simplest form of \(\frac{8}{{12}}\)
Now, \(\frac{{8 \div 4}}{{12 \div 4}} = \frac{1}{3}\)
So, the simplest sort of \(\frac{8}{{12}}\) is \(\frac{1}{3}\)
Resolved Examples – Equivalent Fractions
Q.1. Are the fractions \(\frac{2}{7}\) and \(\frac{4}{{12}}\) same?
Ans: Given fractions are \(\frac{2}{7}\) and \(\frac{4}{12}\)
We see \(2 \times 12 = 7 \multiplication 4\)
\(\Rightarrow 24 \neon 28\)
Therefore, \(\frac{3}{9}\) and \(\frac{4}{12}\) are non equivalent fractions.
Q.2. Are the fractions, \(\frac{9}{7}\) and \(\frac{6}{4}\) equivalent?
Ans: Tending fractions are \(\frac{9}{7}\) and \(\frac{6}{4}\)
We see, \(9 \times 4 = 6 \times 7\)
\(\Rightarrow 36 \NE 42\)
Therefore, \(\frac{9}{6}\) and \(\frac{6}{4}\) are not equivalent fractions.
Q.3. Drop a line fraction equivalent to \(\frac{3}{4}\) with numerator\(15\)
Ans: The given fraction is\(\frac{3}{4}\) which have the numerator \(15\).
Hither, we require to multiply both the numerator and the denominator with \(5\).
So, we have, \(\frac{{3 \times 5}}{{4 \multiplication 5}} = \frac{{15}}{{20}}\)
Consequently, the equivalent divide for \(\frac{3}{4}\) with numerator \(15\) is \(\frac{{15}}{{20}}\).
Q.4. Write \(4\) like fractions for \(\frac{5}{6}.\)
Ans: The given fraction is \(\frac{5}{6}.\)The cardinal equivalent fractions are,
\( \Rightarrow \frac{{5 \times 2}}{{6 \times 2}} = \frac{{10}}{{12}}\)
\( \Rightarrow \frac{{5 \times 3}}{{6 \multiplication 3}} = \frac{{15}}{{18}}\)
\( \Rightarrow \frac{{5 \times 4}}{{6 \multiplication 4}} = \frac{{20}}{{24}}\)
\( \Rightarrow \frac{{5 \times 5}}{{6 \times 5}} = \frac{{25}}{{30}}\)
Therefore, \(\frac{{10}}{{12}},\frac{{15}}{{18}},\frac{{20}}{{24}},\frac{{25}}{{30}}\) are quartet tantamount fractions of \(\frac{5}{6}.\)
Q.5. Write divide equivalent to \(\frac{{36}}{{63}}\) with numerator \(4\).
Autonomic nervous system: The given fraction is \(\frac{{36}}{{63}}\)
Here, we need to divide some the numerator and the denominator aside \(9\).
So, we stick, \(\frac{{36 \div 9}}{{63 \div 9}} = \frac{4}{7}\)
Therefore, the equivalent fraction for \(\frac{{36}}{{63}}\) with numerator \(4\) is \(\frac{4}{7}\)
Q.6. Write \(4\) equivalent fractions for \(\frac{3}{7}.\)
Ans: The given fraction is \(\frac{3}{7}.\) The four equivalent weight fractions are,
\( \Rightarrow \frac{{3 \times 3}}{{7 \times 3}} = \frac{9}{{21}}\)
\( \Rightarrow \frac{{3 \times 7}}{{7 \times 7}} = \frac{{21}}{{49}}\)
\( \Rightarrow \frac{{3 \times 4}}{{7 \multiplication 4}} = \frac{{12}}{{28}}\)
\( \Rightarrow \frac{{3 \times 5}}{{7 \times 5}} = \frac{{15}}{{35}}\)
Therefore, \(\frac{9}{{21}},\frac{{21}}{{49}},\frac{{12}}{{28}},\frac{{15}}{{35}}\) are quaternary equivalent fractions of \(\frac{3}{7}.\)
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Compendious
Two or more fractions representing the same function of a gross are equivalent fractions. To get a fraction equivalent to a given divide, we multiply or divide the numerator and the denominator of the precondition divide by the same not-zero number. In this article, we have learnt in detail about fractions, types of fractions, equivalent fractions, and how to check the equivalent weight fractions.
Ofttimes Asked Questions (FAQs)
Q.1. How do you simplify equivalent fractions?
ANS: To simplify a divide equivalent to a given fraction, we disunite the numerator and the denominator of the apt by the shared, Saame non-zero number.
Deterrent example: The simplest form of equivalent fraction for \(\frac{3}{6}\) is \(\frac{{3 \div 3}}{{6 \div 3}} = \frac{1}{2}\) which is the Combining weight Fraction for \(\frac{3}{6}\).
Therefore, the simplest equivalent divide for \(\frac{3}{6}\) is \(\frac{1}{2}.\)
Q.2. What divide is \(\frac{3}{8}\) equivalent to?
Ans: Some of the equivalent fractions for \(\frac{3}{8}\) are
\(\frac{{3 \times 4}}{{8 \times 4}} = \frac{{12}}{{32}}\)
\(\frac{{3 \times 3}}{{8 \times 3}} = \frac{9}{{24}}\)
\(\frac{{3 \times 5}}{{8 \multiplication 5}} = \frac{{15}}{{40}}\) and \(\frac{{3 \times 7}}{{8 \times 7}} = \frac{{21}}{{56}}\)
So, \(\frac{{12}}{{32}},\,\frac{9}{{24}},\,\frac{{15}}{{40}},\,\frac{{21}}{{56}}\) are same to a fraction \(\frac{3}{8}.\)
Q.3. What is \(\frac{3}{5}\) combining weight to A a fraction?
Ans: Some of the equivalent fractions for \(\frac{3}{5}\)
\(\frac{{3 \times 2}}{{5 \multiplication 2}} = \frac{6}{{10}},\frac{{3 \times 3}}{{5 \times 3}} = \frac{9}{5},\frac{{3 \times 4}}{{5 \multiplication 4}} = \frac{{12}}{{20}}\) and \(\frac{{3 \times 5}}{{5 \times 4}} = \frac{{15}}{{25}}\)
And then, \(\frac{6}{{10}},\frac{9}{{15}},\frac{{12}}{{20}},\frac{{15}}{{25}}\) are like to a fraction \(\frac{3}{5}\)
Q.4. What is an equivalent fraction, with example?
Ans: Two operating room Thomas More fractions representing the same part of a whole are called eq fractions.
\(\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{{10}}\) these fractions are named equivalent fractions.
Q.5. How to find like fractions?
Ans: Multiplying the numerator and the denominator of a fraction by the same cardinal number does non change the value of the fraction.
We have \(\frac{1}{2} = \frac{{1 \times 2}}{{2 \times 2}} = \frac{{1 \multiplication 4}}{{2 \times 4}} = \frac{{1 \times 5}}{{2 \multiplication 5}}.\)
Similarly, \(\frac{{2 \div 2}}{{4 \div 2}} = \frac{{3 \div 3}}{{6 \div 3}} = \frac{{4 \div 4}}{{8 \div 4}} = \frac{{5 \div 5}}{{10 \div 5}} = \frac{1}{2}\)
It shows that dividing the numerator and the denominator of a fraction away the same not-zip number does non change the rate of the fraction.
Q.6. How to try whether cardinal precondition fractions are equivalent surgery not?
Ans: Net ball \(\frac{a}{b}\) and \(\frac{c}{d}\) Be ii given fractions.
Cross multiply the given fractions \(\frac{a}{b} \times \frac{c}{d}\)
If \(advertisement = bc,\) we say that \(\frac{a}{b}\) and \(\frac{c}{d}\) are Equivalent Fractions, otherwise non.
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